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Authors
A. Lj. Juloski; S. Weiland

Identifier
10.3182/20060329-3-AU-2901.00055

Index Terms
hybrid systems,identification,output error models,Bayesian methods

Abstract
In this paper we develop an algorithm for the identification of piecewise linear output error models for the case where the discrete mode of the underlying hybrid system is not known. The presented algorithm is based on a Bayesian framework, i.e. unknown model parameters are treated as random variables and described with probability density functions. The identification problem is posed as a problem of computing the posterior parameter densities, given the prior densities and the observed data. A suboptimal identification algorithm is derived. Operation of the algorithm is demonstrated on an example.

References

[1] Arulampalam, M. S., S. Maskell, N. Gordon and
    T. Clapp (2002). A tutorial on particle filters
    for online nonlinear/non-gaussian bayesian
    tracking. IEEE Transactions on Signal Processing
     50, 174-188.
[2] Bemporad, A., A. Garulli, S. Paoletti and A. Vicino
     (2003). A greedy approach to identification
     of piecewise affine models. In: Hybrid
     Systems: Computation and Control 2003
    (O. Maler and A. Pnueli, Eds.), Vol. 2623 of
    Lecture Notes in Computer Science. Prague,
    Czech Republic. pp. 97-112.
[3] Ferrari-Trecate, G., M. Muselli, D. Liberati and
    M. Morari (2003). A clustering technique for
    the identification of piecewise affine systems.
    Automatica 39(2), 205-217.
[4] Juloski, A. Lj. (2004). Observer Design and Identification
     Methods for Hybrid Systems: Theory
     and Experiments. PhD thesis. Eindhoven
    University of Technology.
[5] Juloski, A. Lj., S. Weiland and W. P. M. H. Heemels
    (2005a). A Bayesian approach to identification
     of hybrid systems. IEEE Transactions on
    Automatic Control. 50, 1520-1533.
[6] Juloski, A. Lj., S. Paoletti and J. Roll (2005b).
    A survey of techniques for identification of
    piecewise affine and hybrid systems. In: Current
     Trends in Nonlinear Systems and Control
     (L. Menini, L. Zaccarian and C. Abdallah,
     Eds.). Birkhauser.
[7] Juloski, A. Lj., W. P. M. H. Heemels, G. Ferrari-Trecate,
     R. Vidal, S. Paoletti and J. H. G.
    Niessen (2005c). Comparison of four procedures
     for the identificaiton of hybrid systems.
     In: Hybrid Systems: Computation and
    Control (M. Morari and L. Thiele, Eds.). Vol.
    3414 of Lecture Notes in Computer Science.
    Springer Verlag. pp. 354-400.
[8] Papoulis, A. (1965). Probability, random variables
    and stochastic processes. McGraw Hill, Inc.
[9] Peterka, V. (1981). Bayesian system identification.
     Automatica 17(1), 41-53.
[10] Roll, J., A. Bemporad and L. Ljung (2004). Identification
      of piecewise affine systems via mixed
     integer programming. Automatica 40, 37-50.
[11] Rosenqvist, F. and A. Karlstrom (2005). Realisation
      and estimation of piecewise-linear
     output-error models. Automatica 41, 545-
     551.
[12] Vidal, R., S. Soatto and S. Sastry (2003). An algebraic
      geometric approach for identification of
     linear hybrid systems. In: Proceedings of 42nd
     IEEE Conference on Decision and Control.